GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_casin.c Lines: 0 8 0.0 %
Date: 2017-11-13 Branches: 0 4 0.0 %

Line Branch Exec Source
1
/*	$OpenBSD: s_casin.c,v 1.8 2016/09/12 19:47:02 guenther Exp $	*/
2
/*
3
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4
 *
5
 * Permission to use, copy, modify, and distribute this software for any
6
 * purpose with or without fee is hereby granted, provided that the above
7
 * copyright notice and this permission notice appear in all copies.
8
 *
9
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16
 */
17
18
/*							casin()
19
 *
20
 *	Complex circular arc sine
21
 *
22
 *
23
 *
24
 * SYNOPSIS:
25
 *
26
 * double complex casin();
27
 * double complex z, w;
28
 *
29
 * w = casin (z);
30
 *
31
 *
32
 *
33
 * DESCRIPTION:
34
 *
35
 * Inverse complex sine:
36
 *
37
 *                               2
38
 * w = -i clog( iz + csqrt( 1 - z ) ).
39
 *
40
 * casin(z) = -i casinh(iz)
41
 *
42
 * ACCURACY:
43
 *
44
 *                      Relative error:
45
 * arithmetic   domain     # trials      peak         rms
46
 *    DEC       -10,+10     10100       2.1e-15     3.4e-16
47
 *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
48
 * Larger relative error can be observed for z near zero.
49
 * Also tested by csin(casin(z)) = z.
50
 */
51
52
#include <complex.h>
53
#include <float.h>
54
#include <math.h>
55
56
double complex
57
casin(double complex z)
58
{
59
	double complex w;
60
	static double complex ca, ct, zz, z2;
61
	double x, y;
62
63
	x = creal (z);
64
	y = cimag (z);
65
66
#if 0
67
	if (y == 0.0) {
68
		if (fabs(x) > 1.0) {
69
			w = M_PI_2 + 0.0 * I;
70
			/*mtherr ("casin", DOMAIN);*/
71
		}
72
		else {
73
			w = asin (x) + 0.0 * I;
74
		}
75
		return (w);
76
	}
77
#endif
78
79
	/* Power series expansion */
80
	/*
81
	b = cabs(z);
82
	if( b < 0.125 ) {
83
		z2.r = (x - y) * (x + y);
84
		z2.i = 2.0 * x * y;
85
86
		cn = 1.0;
87
		n = 1.0;
88
		ca.r = x;
89
		ca.i = y;
90
		sum.r = x;
91
		sum.i = y;
92
		do {
93
			ct.r = z2.r * ca.r  -  z2.i * ca.i;
94
			ct.i = z2.r * ca.i  +  z2.i * ca.r;
95
			ca.r = ct.r;
96
			ca.i = ct.i;
97
98
			cn *= n;
99
			n += 1.0;
100
			cn /= n;
101
			n += 1.0;
102
			b = cn/n;
103
104
			ct.r *= b;
105
			ct.i *= b;
106
			sum.r += ct.r;
107
			sum.i += ct.i;
108
			b = fabs(ct.r) + fabs(ct.i);
109
		}
110
		while( b > MACHEP );
111
		w->r = sum.r;
112
		w->i = sum.i;
113
		return;
114
	}
115
	*/
116
117
	ca = x + y * I;
118
	ct = ca * I;
119
	/* sqrt( 1 - z*z) */
120
	/* cmul( &ca, &ca, &zz ) */
121
	/*x * x  -  y * y */
122
	zz = (x - y) * (x + y) + (2.0 * x * y) * I;
123
124
	zz = 1.0 - creal(zz) - cimag(zz) * I;
125
	z2 = csqrt (zz);
126
127
	zz = ct + z2;
128
	zz = clog (zz);
129
	/* multiply by 1/i = -i */
130
	w = zz * (-1.0 * I);
131
	return (w);
132
}
133
DEF_STD(casin);
134
LDBL_MAYBE_CLONE(casin);